tjohn101 said:Homework Statement
Use the left endpoint graph with the given number of
rectangles to approximate the area bounded by the
curve f (x), the x-axis, and the line x = 4.
f(x)=x2+x
Homework Equations
No idea.The Attempt at a Solution
Once again, not a clue how to start this.
tjohn101 said:Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
What did you do to calculate this? I came up with a different answer.tjohn101 said:Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
Yep, that's really all there is to a problem of this type. You want to split up the interval, calculate the height at whichever point you're using (left, right, mid), calculate the area of each rectangle, and sum them up.tjohn101 said:So for the left endpoints I just do A=b*h and then add them all up?
Same for the right?
The formula for finding the area of a bounded shape is different for each shape. For example, the formula for finding the area of a rectangle is length x width, while the formula for finding the area of a circle is pi x radius squared.
Area is the measurement of the surface inside a shape, while perimeter is the measurement of the distance around the outside of a shape. In other words, area is the amount of space inside a shape, and perimeter is the length of the boundary of a shape.
To find the area of a shape with irregular boundaries, you can break it up into smaller, simpler shapes and find the area of each individual shape. Then, you can add the areas of all the smaller shapes together to find the total area of the irregular shape.
The easiest way to find the area of a triangle is to use the formula: 1/2 x base x height. The base and height of a triangle can be easily measured or calculated, making this formula relatively simple to use.
You can check your answer by using another method to find the area. For example, if you used the formula for finding the area of a rectangle, you can also divide the rectangle into smaller squares and add up their areas to check your answer. Additionally, you can use an online calculator or ask a friend or teacher to verify your answer.